Question

How do you find the greatest common factor of $ 24 $ and $ 28 $ ?

Answer 1

Hint: Greatest common factor is the factor which is common and the largest between the two numbers. It is the largest number which divides them and gives a whole number as an answer. Here, in this equation we need to find the greatest common factor of $ 24 $ and $ 28 $ . In order to solve this question, we will use a prime factorization method to find out the prime factors of $ 24 $ and $ 28 $ . Then, from the prime factors found we will find the common factors and multiply them to get the greatest common factor of $ 24 $ and $ 28 $ .

Complete step-by-step answer:
Here, we are required to find the greatest common factor of $ 24 $ and $ 28 $ .
Firstly, we need to get the prime factors of both the numbers which can be easily done through the prime factorization method. Prime factorization is a way of calculating prime factors which when multiplied gives the original number.
Now, let us first find out the prime factors of $ 24 $ ,
 $ 24 = 2 \times 2 \times 2 \times 3 $ $ $
Now, let us find out the prime factors of $ 28 $ ,
 $ 28 = 2 \times 2 \times 7 $
So, from the prime factorization of both the numbers, it can be said that the common prime factors of both the numbers are $ 2 $ and $ 2 $ .
In order to find the greatest common factor, we have to multiply the common prime factors of both the numbers.
Thus, the greatest common factor is $ 2 \times 2 = 4 $ .
Hence, the greatest common factor of $ 24 $ and $ 28 $ is $ 4 $ .
So, the correct answer is “ $ 4 $ ”.

Note: In this question, we need to note that the greatest common factor is the greatest number that will divide both $ 24 $ as well as $ 28 $ . The number $ 4 $ divides both $ 24 $ and $ 28 $ . The greatest common factor is also known as the highest common factor. Another way of finding the greatest common factor is through ‘listing’.